Elementary Excitations in Bose-Einstein Condensates at Large Scattering Lengths

TL;DR

This paper provides a theoretical analysis of excitation modes in Bose-Einstein condensates at large scattering lengths, showing how Bragg scattering can directly measure the effective two-body potential and proposing a possible transition to a density wave state.

Contribution

It introduces a model fitting recent experimental data and explores the implications of large scattering lengths on excitation spectra and correlations in Bose-Einstein condensates.

Findings

Excellent agreement with experimental data when effective range is small

Bragg scattering measures the Fourier transform of the effective potential at large scattering lengths

Proposes a transition to a density wave state in the condensate

Abstract

We present a theoretical analysis of excitation modes in Bose-Einstein condensates in ultracold alkali-metal gases for large scattering lengths and momenta where corrections to the mean field approximation become important. We assume that the effective interaction in the metastable, single channel, gaseous phase has a well defined Fourier transform that scales with the scattering length. Based on this we show that for increasing scattering lengths or equivalently increasing densities the system becomes less correlated and that at large values of the scattering length Bragg scattering measures directly the Fourier transform of the effective two-body potential. We construct model potentials which fit the recently measured line shifts in $^{85}$Rb by Papp et al. (Phys. Rev. Lett. {\bf 101}, 135301 (2008)), and show that they fix the low momentum expansion of the effective range function. We find excellent agreement with the experimental data when the effective range is $\ll 1$ and the coefficient of the $k^4$-term is $-7.5 \pm 0.5$ in scattering length units. The resolution in Bragg scattering experiments so far does not reveal details of the frequency dependence in the dynamic structure function $S(k,\omega)$ and we show that the Feynman spectrum determines the measured line shifts. We propose the possibility of a transition to a novel density wave state.